12.3 - resistance

what is the resistance of a component?

the potential difference dropped across the component per the current running through it (R = V / I) (i.e., a measure of the difficulty of making current pass through the component)

what is resistance caused by?

the repeated collisions between the charge carriers in the material with each other and the fixed positive ions of the material

charge carriers collide with each other and other fixed positive ions of the material. what does this cause?

resistance

what is the equation linking resistance, potential difference, and current?

R = V / I

what is the unit for resistance?

ohms (Ω)

what is the symbol for resistance?

R

what is an ohm?

• unit of resistance for resistance

• equal to 1 volt per ampere

what is a resistor?

a component desired to have a certain resistance which is the same regardless of the current through it

how do you measure the resistance of a resistor?

here

when measuring the resistance of a resistor, what is the ammeter for?

to measure the current through the resistor, so it can be used in the equation R = V / I to work out resistance

here

when measuring the resistance of a resistor, is the ammeter parallel or in series with the resistor?

in series

here

when measuring the resistance of a resistor, why does the ammeter have to be in series with the resistor?

so the same current passes through both the resistor and the ammeter, otherwise current cannot be used in the equation R = V / I to calculate resistance of the resistor

here

when measuring the resistance of a resistor, what is the voltmeter for?

to measure the potential difference across the resistor

here

when measuring the resistance of a resistor, is the voltmeter parallel or in series with the resistor?

parallel

here

when measuring the resistance of a resistor, why does the voltmeter have to be parallel to the resistor?

• so they have the same potential difference, as the potential difference in each branch is the same for components in parallel, other potential difference can’t be used in R = V / I to determine resistance

• so no current passes through the voltmeter, otherwise the ammeter will not record the exact current through the resistor. putting them in parallel prevents this as a voltmeter has, theoretically, infinite resistance, so no current should be passing through that branch

here

what is the resistance of a voltmeter?

• theoretically, infinite resistance

• in practice, sufficiently high resistance

what is the theoretical resistance of a voltmeter?

infinite

what is the resistance of a voltmeter in practice?

sufficiently high

when measuring the resistance of a resistor, what is the variable resistor for?

to adjust the current and potential difference as necessary, to investigate the variance in current with potential difference

when measuring the resistance of a resistor, how do you investigate the variation of current with potential difference?

using a variable resistor

when measuring the resistance of a resistor, how does a variable resistor investigate the variation of current with potential difference?

• variable resistor adjusted in steps

• at each step, current and potential difference recorded

• measurements can be plotted on a graph of pd against current

HERE GRAPH

what does a graph for a resistor look like?

• linear

• through the origin

• pd against current

• gradient is resistance

• potential difference ∝ current

here

how do you get a graph for a resistor?

• variable resistor adjusted in steps

• at each step, current and potential difference recorded

• measurements can be plotted on a graph of pd against current

here

what is the y-axis on a resistor graph?

potential difference

what is the x-axis on a resistor graph?

current

what is the gradient on a resistor graph? why?

resistance

• y = pd

• x = I

• grad = y / x

• grad = V / I

• R = V / I

how do you find the resistance on a resistor graph?

on any point of the graph, resistance is the potential difference / current, i.e., the gradient

what is the relationship between potential difference and current?

potential difference ∝ current

how do we know that pd ∝ current?

• ohm’s law

• a resistor graph is a straight line through the origin, therefore pd is directly proportional to current

what does ohm’s law state?

the pd across a metallic conductor is proportional to the current through it, provided the physical conditions don’t change

what material does ohm’s law apply to?

metallic conductor

ohm’s law is true, providing what?

the physical conditions (e.g., temperature) don’t change

what are some of the physical conditions that could affect ohm’s law?

temperature, and..?

what is ohmic conductor?

a resistor that follows ohm’s law

if a resistor (ohmic conductor) graph is current against pd, what is the gradient?

1 / resistance

what is a resistivity?

• characteristic feature of a material

• describes the extent to which a material opposes the flow of electric current through it

• ρ = RA / L

what is the equation for resistivity?

ρ = RA / L

• ρ = resistivity

• R = resistance of material

• A = uniform cross-sectional area of conductor

• L = length of conductor

here figure 3 length and cross sectional area

derive the equation ρ = RA / L

• R proportional to L

• R inversely proportional to A

• ρ is a constant for the material

• hence, R = ρL / A

• rearranged, ρ = RA / L

what is the symbol for resistivity?

ρ

what is the unit for resistivity?

ohm metre (Ωm)

how do you find the cross sectional area of a material? (needed when calculating resistivity)

A = πd² / 4

how do you determine the resistivity of a wire?

• measure average diameter of wire using a micrometre to calculate cross sectional area

• measure resistance at different lengths to plot a graph of R against L

• resistivity given by graph’s gradient x A

how do you find the cross sectional area?

• measure the diameter at different point along the wire using a micrometre, and find the mean diameter

• use A = πd² / 4 to find the cross sectional area

how do you find the resistivity on a resistance graph?

gradient x area

what does a resistivity graph look like?

• straight line

• through the origin

• change in resistance against change in length

• gradient = resistivity / area

• resistivity = gradient x area

here

is the resistivity constant or does it fluctuate?

it is constant and characteristic for the material

what is the resistivity of copper?

1.7 × 10^-8 Ωm

what is the resistivity of constantan?

5.0 × 10^-7 Ωm

what is the resistivity of carbon?

3.0 × 10^-5 Ωm

what is the resistivity of silicon?

2300 Ωm

what is the resistivity of PVC?

~ 10¹⁴ Ωm

what is a superconductor?

a wire or device made of material that has zero resistivity at and below a critical temperature that depends on the material’s superconductivity

what is the superconductivity?

the properties (zero resistivity) superconductors have when at or below their critical temperature

when do superconductors experience superconductivity?

when they’re at or below their critical temperature

what is the critical temperature of a superconductor?

it is characteristic to the superconductor

what happens when the superconductor is at or below is critical temperature?

it undergoes no resistivity

what is the graph for a superconductor?

more here …

here

what is the y-axis on the graph for a superconductor?

resistivity

what is the x-axis on the graph for a superconductor?

temperature

what is the shape of the graph for a superconductor?

• lies across the x-axis

• goes straight up at the critical temperature

• linear graph with positive gradient onwards

here

what is the unit of temperature superconductors are measured in?

kelvin, K

what is the benefit of a superconductor having zero resistance?

when a current passes through, there’s no potential difference across it, so the current has no heating effect. this means large currents can be passes through without energy being wasted as heat

what it the benefit of superconductors having no potential difference at critical temperature?

since potential difference is the work done, and work done is energy transferred to different stores. the current has no heating effect when current passes through it, therefore energy isn’t wasted as heat

what are the uses of superconductors?

• used in high power electromagnets that generate very strong magnetic fields

• used in devices such as MRIs, particle accelerators

• used in the development of new applications such as lightweight electric motors and power cables that transfer electrical energy without energy dissipation

what are the benefits of superconductors?

used to make high power electromagnets that generate very strong magnetic fields

what do superconductors generate?

strong magnetic fields

why do superconductors generate large magnetic fields?

because they have large currents passing through them that’s not wasted

what devices are superconductors used for?

• MRIs

• particle accelerators

what new applications are superconductors used in the development of?

• lightweight electric motors

• power cables that transfer electrical energy without energy dissipation

when do superconductors lose its superconductivity?

when its temperature is raised above its critical temperature

what is a high-temperature superconductor?

a superconductor with a critical temperature above 77K, the boiling point of liquid nitrogen

what is the temperature that determines a high temperature superconductor?

77k, the boiling point of liquid nitrogen

what is the boiling point of liquid nitrogen?

77K

what is absolute 0?

• the lowest possible temperature on the thermodynamic (kelvin) scale

• the temperature at which molecules in a substance have no kinetic energy

• 0K, -273.15 °C 

how do you convert kelvin to degrees?

K = C + 273.15

how do you convert degrees to kelvin?

C = K - 273.15

as of 2014, what is the highest critical temperature claimed of a superconductor?

150K - for a compound containing mercury, barium, calcium, copper, and oxygen